The second link goes to a blog post by Greg Sheffield of the Media Research Center that says this:

In its classic "fair and balanced" tradition, CBS slanted in favor of Democrats its poll that found Bush has a 34 percent approval rating and a 59 percent disapproval rating, an all-time high for a CBS poll.

On the bottom of the PDF version of the poll (page 18) it says how many Democrats versus Republicans were contacted.

"Total Republicans" contacted: 272 unweighted and 289 weighted.

"Total Democrats" contacted: 409 unweighted and 381 weighted.

"Total Independents" contacted: 337 unweighted and 348 weighted.

But Sheffield seems to be missing the point. CBS News conducted a random digit dial poll, found that more people identified as Democrats than Republicans, and so they boosted the weight of the Republicans and decreased the weight of the Democrats. Does that sound like liberal bias to you?

More importantly, is this a case of the facts being biased? What if the true number of people in the country who identify as Democrats is actually greater than the number who identify as Republicans? As Gallup points out in a piece criticizing weighting, "the answer to the party identification question may vary for reasons other than sampling error -- including real-world change."

The original CBS numbers -- 27% Republican, 40% Democrat -- do appear to be too Democratic relative to the party ID numbers reported by the major polling houses. The adjusted numbers -- 28% Republican, 37% Democrat -- are a bit closer, but may still be off. (Keep in mind, however, that CBS may use a slightly different party ID question than other houses.)

The point, though, is no one knows the true values of party ID in the electorate right now, and it is likely that more people are self-identifying as Democrats given national trends. Erickson, MacKuen, and Stimson's classic The Macro Polity shows that party ID fluctuates over time in meaningful ways. CBS may be wrong about the exact balance of party ID right now, but Sheffield's claim is just stupid.

Update 2/28: There's an error above. Mystery Pollster points out via email that CBS weights by demographics, not by party, and the demographic weighting has the effect of changing the partisan balance of the study. Here's the relevant verbiage:

At the end of our surveys, we find sometimes that we have questioned too many people from one group or another. Older people, for example, tend to be at home to answer the phone more than younger people, so there is often a greater percentage of older people in our surveys than exists in the American public.

When that happens, we take great pains to adjust our data so that I accurately reflects the whole population. That process is called "weighting." We make sure that our final figures match U.S. Census Bureau breakdowns on age, sex, race, education, and region of the country. We also "weight" to adjust for the fact that people who share a phone with others have less chance to be contacted than people who live alone and have their own phones, and that households with more than one telephone number have more chances to be called than households with only one phone number.

So when we add up all the answers to our questions, we know that no one's opinion counts for more than it should. When you see one of our poll results on TV or in the newspaper, you know that it does not show the opinions of only one or two groups of Americans.

But in any case, my point stands -- why is using a demographic procedure that weights up the number of Republicans evidence of liberal bias?

Update 2/28: In a post on his site, MP finds that the precise partisan balance of the survey does not appear to be driving the results:

Some will no doubt seize on the fact that the latest CBS News sample is a few points more Democratic on party ID (37%) than on their last three surveys (34% in late January, 33% in early January and 32% in December), although the Republican percentage (28%) is about the same as the last three surveys (27%, 29% and 28% respectively). However, the difference in the party results does not explain the drop in the Bush job rating, which occurs across all three categories.

In fact, even when MP recalculates the CBS job approval results for the most recent survey using the average party composition reported on their last three surveys (33% Democrat, 28% Republican, 39% independent or other), the Bush approval percentage still rounds to 34%. The reason is that my recalculation just increases the number of independents at the expense of Democrats. However, Bush's rating is now so low among both subgroups as measured by CBS that the adjustment makes little difference.

He also points out that three new surveys show significant declines in Bush approval:

All three survey organizations now show President Bush with a statistically significant decline in his job approval rating since their last survey:

-CBS News shows an eight point decline Bush's approval rating, from 42% in late January to 34% on the most recent survey.
-RT Strategies shows a seven point decline, from 47% approval in late January to 40% now.
-Rasmussen's average result has declined from 47% earlier in February to 44% over the last six days.

Tabulations of the Bush rating by party identification show that the declines cut across all partisan groups in both surveys.

"CBS News conducted a random digit dial poll, found that more people identified as Democrats than Republicans, and so they boosted the weight of the Republicans and decreased the weight of the Democrats. Does that sound like liberal bias to you?"

In a word, yes.

If 37% of people ID themselves as Dems, 37% as Repubs, and the rest are independents, then a poll that oversamples Dems is not representative of overall public sentiment. It is skewed to the left. It certainly doesn't help that the poll is conducted by CBS and The New York Times - two media agencies that are more hostile to Republicans than many others.

You would cry foul too if a poll that oversampled Repubs produced an oddly low likeability/approval rating for a Democrat.

Still, I should point out that we're talking about a negligible difference in favorability considering that the correct percentages of Repubs/Dems would only raise Bush's approval rating to around 40% - a dip that is sadly common for this point in a second term presidency.

On another note, you wrote:

"The point, though, is no one knows the true values of party ID in the electorate right now, and it is likely that more people are self-identifying as Democrats given national trends."

Random polling of adults will almost always suggest that the public is increasingly aligning itself with the party in the minority whenever names are left out. However, when likely voters are polled, and when candidates' names are mentioned, the percentages of Dems/Repubs flows back to around 37% each. You shouldn't make the mistake of thinking that just because there is a very vocal Bush-hating crowd, that their message resonates with the average American voter. It doesn't.

Why would we assume it's 37% each? Of the three major poll houses who released annual numbers for 2005 (in the Mystery Pollster post linked above), 2 of 3 found more Dems than Republicans. In addition, party affiliation has moved dramatically over longer time periods - there's no reason to assume it will stay static.